Extrinsic geometric properties of shortest geodesics in a neighborhood about a point of strict tangency

The concept of a point of strict tangency of an $m$-dimensional surface lying in an $n$-dimensional Euclidean space $\mathbf{E}^n$ is formulated using the language of limit sets. It is proved that a point of strict tangency of a surface is also a point of strict tangency for each of the shortest geodesies passing through it.